How Long Does It Take for a Mass to Freeze or Melt?

[Mayhem]

Homework Statement

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Relevant Equations

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Hello.

We all know $Q = mc\delta t$, but is there an equation which describes the time it takes for a mass to freeze/melt given a certain specific heat capacity? This way you could for example quantify how long it takes room temperature to freeze in a freezer (or any element).

 

[BvU]

how long it takes room temperature to freeze

If by 'freezing' you mean 'change from liquid phase to solid phase', then room temperature does not freeze.

The $\ Q = \dot m\,c_p\,\Delta t\$ equation doesn't fly (for a pure substance $\ \Delta t= 0\$ , i.e. the phase change takes place at the freezing/melting point) .

Instead, a material-dependent heat of melting has to be removed (c.q. supplied for melting), so at best you have $\ Q = \dot m\,\Delta H_{fus}\$.

How fast it goes depends on a whole lot of factors.

$\$

 

[haruspex]

The $\ Q = \dot m\,c_p\,\Delta t\$ equation doesn't fly (for a pure substance $\ \Delta t= 0\$ , i.e. the phase change takes place at the freezing/melting point) .

I think t is time here.
@Mayhem, having got, say, a tank of water to 0C, the time it takes to freeze it all depends on the applied cooler temperature, where it is applied, the conductivities of water and ice, and the convection within the tank.